The amp is rated 200 W, so that is what te cord should be sized for.
The 200 W is based on RMS values
V and I peak / sqrt2
P = Vp/sqrt2 x zip/sqrt2 = Vp Ip / 2
An 'average' value
So peak is 2 x average in this case
Bathe load is reactive so an estimate of power factor + eff is ~0.5
Peak VA = 2 x 200 / 0.5 = 800 VA
But to your point. Yes, draw will typically be fractions of an amp and likely more that 5 under transient conditions.
I haven't had to do this in a long time, so again, I don't want to encourage anybody to be unsafe with electricity. I believe the rule is that you can use a factor of 8x or 12x (whichever it is) as long as there is an appropriate breaker or fuse to prevent a fire should you actually go over. You would be able to use a cord rated as low as ~20 watts on a 200 watt amp if and only if there were a fuse/breaker between the amp and mains that would trip at nominal 20 watts. I say nominal because those disconnects all have a slope. Otherwise you would need a cord rated for 200watts.
You are within safety specs running up to ~12kwatts on a 15amp circuit (120V North America) with just the breaker (no intermediate disconnects). It will be safe because the breaker is there. It will work because of the slope of the breaker (drawing the full 12kwatts for a millisecond won't trip the breaker).
Note that the fuses in the amps don't count. Because they are "closer" to the amp than the power source.
If you could find say a power strip that connected to mains with a 15amp breaker *and* 0.2 amp fuses on each outlet, you would be within code to use a lower rated power cord (since the fuses are closer to mains than the load). Unfortunately I could not find such a device probably because it's cheaper and easier to buy IEC cords!
I didn't bring this up to encourage people to do silly things especially when power cords are so cheap.
If somebody had say 2xSVS SB2000 with 1100watts peak power and a Behringer A800 (800 watts) they might think that they need multiple 15 amp circuits and, in the worst case, could end up paying the electrician for additional drops and achieve nothing but introducing ground loop noise!
As far as I know (and please correct me if I'm wrong as we really do want to avoid unsafe situations), that whole 3000 watt load can be put into a single 15amp (US 120volt) circuit along with the TV and AVR with no safety issue and no risk of tripping the breaker. However, if you put it on the same circuit as the microwave, that's a different story.
These things used to matter in pro audio but not home theater or hifi. Now we suddenly have stereo amplifiers that can put out 600wpc (Nord 28) and suddenly we need to manage power as if we are setting up pro audio.